## Results (displaying matches 1-50 of 226) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
180.1.f.a $$2$$ $$0.090$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-15})$$ $$\Q(\sqrt{15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots$$
180.1.m.a $$4$$ $$0.090$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$$
180.1.p.a $$2$$ $$0.090$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$-1$$ $$-1$$ $$1$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$$
180.1.p.b $$2$$ $$0.090$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$1$$ $$-1$$ $$-1$$ $$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$$
180.2.a.a $$1$$ $$1.437$$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$2$$ $$-$$ $$q+q^{5}+2q^{7}+2q^{13}+6q^{17}-4q^{19}+\cdots$$
180.2.d.a $$2$$ $$1.437$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+i)q^{5}+2iq^{7}+4q^{11}-2iq^{17}+\cdots$$
180.2.e.a $$8$$ $$1.437$$ 8.0.18939904.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{4}-\beta _{5}+\beta _{7})q^{4}+\cdots$$
180.2.h.a $$4$$ $$1.437$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{2}+2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{8}+\cdots$$
180.2.h.b $$8$$ $$1.437$$ 8.0.3317760000.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{3}q^{4}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$$
180.2.i.a $$2$$ $$1.437$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$-1$$ $$1$$ $$q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$$
180.2.i.b $$6$$ $$1.437$$ 6.0.954288.1 None None $$0$$ $$-1$$ $$3$$ $$-3$$ $$q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$$
180.2.j.a $$4$$ $$1.437$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2-2\zeta_{8}^{2})q^{7}+\cdots$$
180.2.k.a $$2$$ $$1.437$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$2$$ $$0$$ $$q+(-1-i)q^{2}+2iq^{4}+(1-2i)q^{5}+\cdots$$
180.2.k.b $$2$$ $$1.437$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+(1+i)q^{2}+2iq^{4}+(-1+2i)q^{5}+\cdots$$
180.2.k.c $$2$$ $$1.437$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$4$$ $$0$$ $$q+(1+i)q^{2}+2iq^{4}+(2-i)q^{5}+(-2+\cdots)q^{8}+\cdots$$
180.2.k.d $$8$$ $$1.437$$ 8.0.157351936.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(2\beta _{4}+\cdots)q^{5}+\cdots$$
180.2.k.e $$12$$ $$1.437$$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots$$
180.2.n.a $$4$$ $$1.437$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$-6$$ $$6$$ $$6$$ $$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
180.2.n.b $$4$$ $$1.437$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$6$$ $$6$$ $$-6$$ $$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots$$
180.2.n.c $$8$$ $$1.437$$ 8.0.3317760000.8 $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+\beta _{1}q^{3}+2\beta _{3}q^{4}-\beta _{2}q^{5}+\cdots$$
180.2.n.d $$48$$ $$1.437$$ None None $$0$$ $$0$$ $$-18$$ $$0$$
180.2.q.a $$48$$ $$1.437$$ None None $$0$$ $$0$$ $$0$$ $$0$$
180.2.r.a $$12$$ $$1.437$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{9}q^{5}+(-\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{7}+\cdots$$
180.2.w.a $$24$$ $$1.437$$ None None $$0$$ $$-2$$ $$0$$ $$0$$
180.2.x.a $$128$$ $$1.437$$ None None $$-2$$ $$0$$ $$-4$$ $$0$$
180.3.b.a $$4$$ $$4.905$$ $$\Q(\sqrt{-2}, \sqrt{23})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{2}q^{7}+7\beta _{1}q^{11}+\cdots$$
180.3.c.a $$4$$ $$4.905$$ $$\Q(\zeta_{10})$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{10}q^{2}+(-1+\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{4}+\cdots$$
180.3.c.b $$8$$ $$4.905$$ 8.0.85100625.1 None None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots$$
180.3.c.c $$8$$ $$4.905$$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2-\beta _{4})q^{4}+\beta _{3}q^{5}+2\beta _{6}q^{7}+\cdots$$
180.3.f.a $$1$$ $$4.905$$ $$\Q$$ $$\Q(\sqrt{-5})$$ None $$-2$$ $$0$$ $$5$$ $$4$$ $$q-2q^{2}+4q^{4}+5q^{5}+4q^{7}-8q^{8}+\cdots$$
180.3.f.b $$1$$ $$4.905$$ $$\Q$$ $$\Q(\sqrt{-5})$$ None $$2$$ $$0$$ $$5$$ $$-4$$ $$q+2q^{2}+4q^{4}+5q^{5}-4q^{7}+8q^{8}+\cdots$$
180.3.f.c $$2$$ $$4.905$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+iq^{2}-4q^{4}+(-3-2i)q^{5}-4iq^{8}+\cdots$$
180.3.f.d $$4$$ $$4.905$$ $$\Q(\sqrt{-3}, \sqrt{22})$$ None None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
180.3.f.e $$4$$ $$4.905$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(2+2\zeta_{12}^{2})q^{4}+\cdots$$
180.3.f.f $$4$$ $$4.905$$ $$\Q(i, \sqrt{15})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(4+\beta _{3})q^{4}+5\beta _{2}q^{5}+(3\beta _{1}+\cdots)q^{8}+\cdots$$
180.3.f.g $$4$$ $$4.905$$ $$\Q(\sqrt{-3}, \sqrt{22})$$ None None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
180.3.f.h $$8$$ $$4.905$$ 8.0.$$\cdots$$.4 None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$$
180.3.g.a $$4$$ $$4.905$$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None None $$0$$ $$0$$ $$0$$ $$-16$$ $$q-\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(-\beta _{1}-6\beta _{2}+\cdots)q^{11}+\cdots$$
180.3.l.a $$2$$ $$4.905$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$6$$ $$-14$$ $$q+(3-4i)q^{5}+(-7-7i)q^{7}-10q^{11}+\cdots$$
180.3.l.b $$4$$ $$4.905$$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$-12$$ $$20$$ $$q+(-3-2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(5+2\beta _{1}+\cdots)q^{7}+\cdots$$
180.3.l.c $$4$$ $$4.905$$ $$\Q(i, \sqrt{10})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+(3\beta _{2}-\beta _{3})q^{11}+\cdots$$
180.3.m.a $$4$$ $$4.905$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}+3\zeta_{8}^{3})q^{5}+\cdots$$
180.3.m.b $$4$$ $$4.905$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}-3\zeta_{8}^{3})q^{5}+\cdots$$
180.3.m.c $$40$$ $$4.905$$ None None $$0$$ $$0$$ $$0$$ $$0$$
180.3.o.a $$4$$ $$4.905$$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None None $$0$$ $$-6$$ $$0$$ $$8$$ $$q+(-3+3\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$$
180.3.o.b $$12$$ $$4.905$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$2$$ $$0$$ $$-6$$ $$q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{1}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots$$
180.3.p.a $$4$$ $$4.905$$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ None $$-4$$ $$4$$ $$10$$ $$4$$ $$q+(-2+2\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots$$
180.3.p.b $$4$$ $$4.905$$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ None $$4$$ $$-4$$ $$10$$ $$-4$$ $$q+(2-2\beta _{2})q^{2}+(\beta _{1}-2\beta _{2}-\beta _{3})q^{3}+\cdots$$
180.3.p.c $$128$$ $$4.905$$ None None $$0$$ $$0$$ $$-22$$ $$0$$
180.3.s.a $$96$$ $$4.905$$ None None $$0$$ $$0$$ $$0$$ $$0$$
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